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News

October 2024

In this edition of the News you will find:

Red Square  Explicit Teaching:
     Opportunity or Opportunity Lost?

Red Square  Poly Plug Spring Sale

Red Square  Get to Know a Cameo
     ... Find My Pattern
     ... See-Saw

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  • Explicit Teaching: Opportunity or Opportunity Lost?

    Explicit teaching seems to have become a trendy expression recently. Without further investigation those words suggest encouraging teaching that is clear and easy to understand. However, if that's the case, why are they popping up more often? Clear and easy to understand is every teacher's aim/hope for every lesson.

    Perhaps that aim is exactly the reason why the words are popping up. Clear and easy to understand is every teacher's aim, and to achieve it every teacher makes teaching craft choices when planning and executing a lesson. Perhaps Explicit Teaching is a new catch phrase for encouraging teachers to make those choices based on a broader range of pedagogies.

    For example, a list such as Lesson Features, which has been developed over time through the participation of scores of teachers in practical, classroom-based workshops in response to the question:

    What are the learning features in this activity likely to fascinate, captivate and absorb my students?

     

    See Link List below to print the PDF version.

    If a focus on Explicit Teaching is an opportunity intended to support teachers to become increasingly conscious of, and confident in, choosing pedagogies as part of planning, executing and reviewing each lesson, that would be a significant positive for mathematics teaching and learning.

    But so far these thoughts are supposition. Time for further investigation.

    These words from the NSW Department of Education were listed first for my web search on 'explicit teaching':

    Explicit teaching practices involve teachers clearly showing students what to do and how to do it, rather than having students discover that information themselves.
    which concerned me a little - not for what it includes, but for what it excludes.

    Showing students what to do and how to do it is a legitimate strategy - sometimes - but to place it in opposition to students discovering information for themselves - a pedagogy that is at least equally valuable - could hardly be described as inclusive education. The statement implies excluding from learning those students who prefer to sometimes learn for themselves. Students like any one of the young people in these examples (see Link List below for sources):

    From a conversation with Andy Wain
    February 1996

    Garden Beds is my favourite problem at the moment. I have one year 8 student who typically gets 2 out of 20 in class tests. However in the task centre, with a little intervention from me, this girl was able to generalise the problem for n plants in r rows. She wouldn't leave the problem alone.

    I got more work from her than I ever would in class and I learnt more about her true abilities.

    from Clients' Newsletter #3, April 1996
    Photo from Maths At Home Garden Beds

    In early 2007 Per Berggren introduced Star Numbers to his Year 9 class on a Friday. Helena became so engrossed that she just kept working on it all weekend. She handed in a stunning report early the next week - just because she wanted to. Star Numbers wasn't in our Task Library at the time, but by mid-2008, inspired by Helena, it was. You can meet Helena and find her report in the Star Numbers cameo.

    While we're in Year 9, reconsider the work of the Year 9 girl in the video we introduced in the previous news issue. She created the problem for herself as she was playing around with Poly Plug in her own time, worked it out for herself over several months, and was so excited by finding a pattern that she made a video to share her learning. Her teaching is quite explicit - clear and easy to understand - partly because of the way she tells the viewer and partly because of the concrete and visual nature of the presentation. A combination of teaching craft choices working together to encourage learning.

    Explore either of the two Task Cameos listed below for this month.

    Task 10, Find My Pattern, is a task wholly created by a group of Year 4 students. The class had been working on number patterns and the teacher had encouraged students to make their own. The children also had opportunity in the week to work in pairs with hands-on tasks they chose for themselves. This group synthesised the two experiences and the outcome is we all have a new task in the library.

    Task 58, See-Saw, includes a story from a remote Aboriginal school of a couple of students in the class using this task, others becoming fascinated and, at break time, all the students gathering in the playground, of their own volition, to explore the mathematics for themselves with the real see-saw.

    Surely no education department would want to promote a particular teaching strategy that implies exclusion of experiences like these from the teaching and learning tapestry of mathematics?
    And indeed, perhaps the NSW department didn't intend that since, as evidenced by this breadcrumb trail to the reference, it is found deep in the primary reading section of the Literacy and Numeracy part of the site.

    Home > Teaching and learning > Curriculum > Literacy and numeracy > Resources for schools > What works best > What works best: Reading K-6 > Theme 2 > Explicit teaching

    Could it be that Explicit Teaching is a teaching craft tool designed for learning to read, rather learning to work like a mathematician?

    My search page results had other references from the NSW system and its Victorian equivalent and the Australian Education Research Organisation and more. They all suggest that Explicit Teaching is a highly structured teaching strategy and use phrases such as 'powerful, evidence-based teaching', 'show students what to do and how to do it', 'breaks down what students need to learn into smaller learning outcomes and models each step'.

    All this may be so, but why must there be a revolution-style incursion into the way teachers are currently making excellent and appropriate teaching craft choices using an equally well researched, evidenced-based range of learning features?

    No one believes that just one teaching strategy in mathematics education - even computer-guided individualised learning - is going to encourage the best mathematics learning for all students at all times. So why try to introduce improvement with an approach that creates that impression?

    Sadly, the reason for the words Explicit Teaching trending is a massive investment in documents - and diagrams - which, by the extent of funding and weight of text, implies that teachers pedagogical choices until now have been, if not the root of all problems in mathematics education, at least misguided. Opportunity lost.

    An opportunity gained would be to invest directly in teachers in ways that bring them together to explore, discover, discuss, plan, trial, reflect, evaluate, document; in a way that values each teacher for who they are and the experience they share. Teachers working with teachers will always bring more lasting change outcomes than imposition. Teachers are the best resource we have in education.

    At the same time as I was thinking about and researching the ET trend, The Common Denominator, a magazine for members of The Mathematical Association of Victoria (MAV), arrived in the post. Its lead article is co-written by David Howes, Deputy Secretary, Department of Education, Victoria and Jen Bowden, MAV CEO. It led me back to imagining hopeful thoughts about the ET trend.

    In the article 'Teaching Mathematics in Victoria' David relates a recent experience working for a day as a relief teacher "...at one of our most disadvantaged primary schools.". The teacher's daily outline included a video about two and three dimensions which David used. Part way through it he realised that neither he nor the students followed the explanation so he turned off the video and "...sat down on one of the small chairs and had a go at explaining...".

    Confirmation that it is okay to change tack in the middle of a lesson if the detailed planning isn't going as planned. Confirmation too that Plan B didn't have to be detailed in advance. Experience was kicking in here and David was now working 'on his feet' from the seat of a small chair.

    Unfortunately the article doesn't explain what having a go at explaining meant. The theme of the article is Explicit Teaching, so are we to suppose that he proceeded to tell students 'what to do and how to do it' as he understands it for the content of two and three dimensions?

    Perhaps, but the article also supports imagining an alternative. In his own words, "Explicit teaching does not mean there is no place for inquiry-based learning and problem solving.".

    Perhaps instead of telling, he began an inquiry into 2D and 3D space by asking the children what they thought 2D and 3D meant. Perhaps the learning experience went on from there to physically explore the familiar, being the upness, downness, leftness, rightness, forwardness, backwardness and all-aroundness of the 3D world of the classroom, before raising a problem posing question such as: Oh no, it's the end of the world as we know it! All its upness and downness is being taken away by aliens. We're trapped in this room. What can we do to survive?.

    So much more can grow from a start like this and perhaps David did do something along these lines, after all, again in his own words, "It (explicit teaching) certainly does not mean there is no place for supporting and enabling student curiosity, reasoning and questioning.".

    He would also be aware that one of the critical elements of learning through physical involvement is the follow up activity in which groups of students re-examine the experience by being challenged to build a table top model to re-create it. Imagine your table top is our classroom floor. Find things around the classroom that will help you explain what it would be like if you had to live flat on the floor.. This second look encourages re-enacting, re-thinking and re-expressing which strengthens learning.

    Further, in his paragraph numbered 3. Explicit Teaching, David suggests that "Explicit teaching involves collaborative planning to ensure teaching and learning is..." effectively sequenced and he offers "...concrete to pictorial to abstract..." as an example sequence.

    Given he was working as a relief teacher this day, he would not have had the opportunity for collaborative planning. However, his previous teaching experiences and his awareness of lesson features which encourage learning, one of which is the pedagogical value of students recording and writing about their mathematical experiences, would likely have led to a plenary discussion of the lesson, recording key points as they arose and the invitation to students to write and draw in their maths journal.

    Imagining David in the classroom situation he introduced has actually led to considerable thought about "...the teacher's right to choose from a variety of pedagogies that can meet their students' learning needs." (Jen Bowden in the same article). One of these is ET. Opportunity regained.

  • Poly Plug Spring Sale

    • Normally $11 - $13·50 depending on number.
    • Pembroke Primary School were the first to take advantage. They intended to order 11, but were able to order 15 for the same price.
    • Sale ends December 1st unless stock runs out.
    • Use Poly Plug in Link List below as the starting point for discovering the many, many ways teachers use this resource.

    Use order form in Link List below.
    Include a purchase order number or Visa/Mastercard details.

  • Get to Know a Cameo

    Task 10, Find My Pattern
    A group of Year 4 students created this problem, so watch out! It's likely to be sneaky. They give us the first and last numbers in a pattern and show us how many numbers are missing between these limits. We're even given a set of numbers from which the answers must come.

    All we have to do is recreate the sequence.

    Mmm, now look at the first pathway on the card. Start at 11 and finish at 8 putting 5 numbers between to make a pattern. Yep, this could indeed be tricky.

    Take a moment before you start to consider the pedagogy here. This problem could be presented as a pencil and paper exercise, but it isn't. What advantages do you see in its concrete presentation? Any advantages to the story shell introduction, which is true? It's a task from our library so it's designed to be used by pairs of students. Compare and contrast with a pencil and paper, do your own work, because the teacher has chosen it, type of presentation.

    The Task Cameo not only provides answers to the sneaky two step patterns the children created, but it also explores ways to work them out and suggests there is something else exciting to discover if the pattern is represented by ordered pairs.

    In the eTask Package this task is in the 'easy' set because it only requires a few counters that fit into the cells on the card.

    Task 58, See-Saw
    The mathematics behind this task is straight out of a physics classroom. However, although it may be appropriate to introduce it with some students who use this task, exposing the mathematical formulas is not the objective of the task. Rather, the intent is to explore the variables that might influence making the see-saw balance, and developing a sense of how they work together to do that.

    One of the challenges in a mathematician's work is to be able to explain their discoveries to colleagues - and perhaps the world. This is the challenge that students are invited to accept when they have carried out the experiments on the card, and possibly more of their own.

    The Task Cameo includes a story from a remote Aboriginal school where the students carried out many more experiments than expected using the see-saw in the playground. Also in the cameo, should you need it, is support for applying the mathematical equations related to creating the balance.

    In the eTask Package this task is in the 'easy to make' set because it only requires few common objects which are either findable around school or easily obtainable.

Keep smiling,
Doug.
Green Line

Link List

  • Did you miss the Previous News?
    If so you missed information about:
    1. Teachers Are The Best Resource
    2. Student's Cube Tube Video
    3. Something New in Eric The Sheep
    4. Choosing Teaching Craft
    5. Get to Know a Cameo
      ... Window Frames, Have A Hexagon

Did You Know?

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